Loïc Denis

Inverse problems approaches for digital hologram reconstruction

Digital holography (DH) is being increasingly used for its time-resolved three-dimensional (3-D) imaging capabilities. A 3-D volume can be numerically reconstructed from a single 2-D hologram. Applications of DH range from experimental mechanics, biology, and fluid dynamics. Improvement and characterization of the 3-D reconstruction algorithms is a current issue. Over the past decade, numerous algorithms for the analysis of holograms have been proposed. They are mostly based on a common approach to hologram processing: digital reconstruction based on the simulation of hologram diffraction. They suffer from artifacts intrinsic to holography: twin-image contamination of the reconstructed images, image distortions for objects located close to the hologram borders. The analysis of the reconstructed planes is therefore limited by these defects. In contrast to this approach, the inverse problems perspective does not transform the hologram but performs object detection and location by matching a model of the hologram. Information is thus extracted from the hologram in an optimal way, leading to two essential results: an improvement of the axial accuracy and the capability to extend the reconstructed field beyond the physical limit of the sensor size (out-of-field reconstruction). These improvements come at the cost of an increase of the computational load compared to (typically non iterative) classical approaches.

Quantitative phase retrieval reconstruction from in-line hologram using a new proximal operator: application to microscopy of bacteria and tracking of droplets

Phase retrieval reconstruction is a central problem in digital holography, with various applications in microscopy, biomedical imaging, fluid mechanics. In an in-line configuration, the particular difficulty is the non-linear relation between the object phase and the recorded intensity of the holograms, leading to high indeterminations in the reconstructed phase. Thus, only efficient constraints and a priori information, combined with a finer model taking into account the non-linear behaviour of image formation, will allow to get a relevant and quantitative phase reconstruction. Inverse problems approaches are well suited to address these issues, only requiring a direct model of image formation and allowing the injection of priors and constraints on the objects to reconstruct, and hence offer good warranties on the optimality of the expected solution. In this context, following our previous works in digital in-line holography, we propose a regularized reconstruction method that includes several physicallygrounded constraints such as bounds on transmittance values, maximum/minimum phase, spatial smoothness or the absence of any object in parts of the field of view. To solve the non-convex and non-smooth optimization problem induced by our modeling, a variable splitting strategy is applied and the closed-form solution of the sub-problem (the so-called proximal operator) is derived. The resulting algorithm is efficient and is shown to lead to quantitative phase estimation of micrometric objects on reconstructions of in-line holograms simulated with advanced models using Mie theory. Then we discuss the quality of reconstructions from experimental inline holograms obtained from two different applications of in-line digital holography: tracking of an evaporating droplet (size~100μm) and microscopy of bacterias (size~1μm). The reconstruction algorithm and the results presented in this proceeding have been initially published in [Jolivet et al., 2018].1

Improving color lensless microscopy reconstructions by self-calibration

Lensless color microscopy is a recent 3D quantitative imaging method allowing to retrieve physical parameters characterizing microscopic objects spread in a volume. The main advantages of this technique are related to its simplicity, compactness, low sensitivity of the setup to vibrations and the possibility to accurately characterize objects. The cost-effectiveness of the method can be further increased using low-end laser diodes as coherent sources and CMOS color sensor equipped with a Bayer filter array. However, the central wavelength delivered by this type of laser is generally known only with a limited precision and can evolve because of its dependence on temperature and power supply voltage. In addition, Bayer-type filters of conventional color sensors are not very selective, resulting in spectral mixing (crosstalk phenomenon) of signals from each color channel. Ignoring these phenomena leads to significant errors in holographic reconstructions. We have proposed a maximum likelihood estimation method to calibrate the setup (central wavelength of the laser sources and spectral mixing introduced by the Bayer filters) using spherical objects naturally present in the field of view or added (calibration objects). This calibration method provides accurate estimates of the wavelengths and of the crosstalk, with an uncertainty comparable to that of a high-resolution spectrometer. To perform the image reconstruction from color holograms following the self-calibration of the setup, we describe a regularized inversion method that includes a linear hologram formation model, sparsity constraints and an edge-preserving regularization. We show on holograms of calibrated objects that the self-calibration of the setup leads to an improvement of the reconstructions.

Innovative real-time processing for solar adaptive optics

Themis is a 90 cm solar telescope which undergoes a rejuvenation of its scientific instruments. In particular, it is about to be equipped with an adaptive optics (AO) system with a bandwidth of at least 1 kHz and featuring a 97 actuator deformable mirror and 10×10 Shack-Hartmann wavefront sensor. Nowadays, the computational power required by such a system can be provided by current multi-core CPU. We have therefore implemented from scratch the real-time control system in pure software using Julia,1 a new language for technical computations, and running on Linux OS. Our main motivation was to be able to exploit new advances in wavefront sensing and adaptive optics control. With a computational cost comparable to state-of-the-art but sub-optimal methods used in solar AO, our wavefront sensing algorithm estimates the local slopes and their covariances following a maximum likelihood registration method. Themis AO system has a modest size but can be used to assert the benefits of maximum a posteriori (MAP) wavefront sensing and control,2, 3 of accounting of the covariances of the measure and of the temporal correlation of the turbulent wavefront.

Exoplanet detection in angular and spectral differential imaging: local learning of background correlations for improved detections

The search for new exoplanets by direct imaging is a very active research topic in astronomy. The detection is particularly challenging because of the very high contrast between the host star and the companions. They thus remain hidden by a nonstationary background displaying strong spatial correlations. We propose a new algorithm named PACO (for PAtch COvariances) for reduction of differential imaging datasets. Contrary to existing approaches, we model the background correlations using a local Gaussian distribution that locally captures the spatial correlations at the scale of a patch of a few tens of pixels. The decision in favor of the presence or the absence of an exoplanet in then performed by a binary hypothesis test. The method is completely parameter-free and produces both stationary and statistically grounded detection maps so that the false alarm rate, the probability of detection and the contrast can be directly assessed without post-processing and/or Monte-Carlo simulations. We describe in a forthcoming paper its detailed principle and implementation. In this paper, we recall the principle of the PACO algorithm and we give new illustrations of its benefits in terms of detection capabilities on datasets from the VLT/SPHERE-IRDIS instrument. We also apply our algorithm on multi-spectral datasets from the VLT/SPHERE-IFS spectrograph. The performance of PACO is compared to state-of-the-art algorithms such as TLOCI and KLIP-PCA.